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Abstract

We study the problem of recursive utility maximization in the presence of nonlinear constraint on the wealth for a model driven by L evy processes. We extend the notion of W-divergence to vector valued functions and then reduce the problem to the classical problem of recursive utility maximization problem under the W -projection. Using BSDE technics, we derive a first order condition which gives a necessary and sufficient condition of optimality under the W-projection, which generalizes the characterization of optimal solution obtained in [6] in the case of continuous time, and also the result obtained in [9] in the case of standard utility.